Geology 3120 Geology 3120 -- Failure ModelsFailure Models

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OutlineOutline

• Virtual rock deformation experiment

• Influence of pore fluid pressure

• Andersonian faulting

• Byerlee’s law

• Other failure models

Virtual Rock Deformation ExperimentVirtual Rock Deformation Experiment

Run σ1 (MPa) σ3 (Mpa) Failure (Θ)1 250 150 none2 250 50 +37°3 490 190 +37°4 690 310 +37°

σσ11

σσ11

σσ33

+Θ+Θ

Run 1: Run 1: σσ11= 250 = 250 MPaMPa; ; σσ33=150 =150 MPaMPa; no fracture; no fracture

Run 1: Run 1: σσ11= 250 = 250 MPaMPa; ; σσ33=150 =150 MPaMPa; no fracture; no fracture

Run 2: Run 2: σσ11= 250 = 250 MPaMPa; ; σσ33= 50 = 50 MPaMPa; 37° fracture; 37° fracture

Run 2: Run 2: σσ11= 250 = 250 MPaMPa; ; σσ33=150 =150 MPaMPa; no fracture; no fracture

74°

Run 3: Run 3: σσ11= 490 = 490 MPaMPa; ; σσ33=190 =190 MPaMPa; 37° fracture; 37° fracture

Run 3: Run 3: σσ11= 490 = 490 MPaMPa; ; σσ33=190 =190 MPaMPa; 37° fracture; 37° fracture

74°

Run 4: Run 4: σσ11= 690 = 690 MPaMPa; ; σσ33=310 =310 MPaMPa; 37° fracture; 37° fracture

Run 4: Run 4: σσ11= 690 = 690 MPaMPa; ; σσ33=310 =310 MPaMPa; 37° fracture; 37° fracture

74°

Determining the Failure EnvelopeDetermining the Failure Envelope

φ = 16tan φ = 0.29σ0 = 60 MPaσc = 0.29σn + 60 MPa

φσc = 0.29σn + 60 MPa

Predicting FailurePredicting Failure

Run 5: Run 5: σσ33= 250 = 250 MPaMPa; at what ; at what σσ1 1 fracture occur?fracture occur?

Predicting FailurePredicting Failure

Run 5: Run 5: σσ33= 200 = 200 MPaMPa; at what ; at what σσ1 1 fracture occur?fracture occur?

74°

Influence of Pore Fluid PressureInfluence of Pore Fluid Pressure

Applied Stress

Effective Stress

pf

Pore fluid pressure decreases normal stresses by the fluid pressPore fluid pressure decreases normal stresses by the fluid pressure amount.ure amount.

Rock can then fail under the MohrRock can then fail under the Mohr--Coulomb Law.Coulomb Law.

Principal StressesPrincipal Stresses

• σ1 - greatest principal stress

• σ2 - intermediate principal stress

• σ3 - minimum principal stress• Principal stress directions are mutually perpendicular to each other

Conjugate FaultsConjugate Faults

Most simply - two fault planes that intersect to form a straight line

Perhaps more typical - two fault surfaces that intersect to form a line

Acute angle - < 90° angle

Obtuse angle - > 90° angle

Acute

Obtuse

Assumptions for Assumptions for AndersonianAndersonian FaultingFaulting

σn

σc

σn

Y = Y = mXmX + b+ b

(

(

• Coulomb brittle failure - no pre-existing faults

• φ = 90 - 2Θ

• Most rocks have φ = 30° so Θ = ±30°

Assumptions for Assumptions for AndersonianAndersonian FaultingFaulting

Normal stress (σ1 , σ2, σ3)

Zero shear stress

• No shear stress exists at the Earth’s surface

• One principal stress must act normal to the surface

• σ1 , σ2, or σ3 must be perpendicular to the surface

Rules of Thumb for StressesRules of Thumb for Stresses

• σ1 bisects the acute angle

• σ2 is parallel to the intersection of conjugate faults

• σ3 bisects the obtuse angle

Normal FaultNormal Fault

StrikeStrike--slip Faultslip Fault

Thrust FaultThrust Fault

SouthSouth NorthNorthNormal faultingNormal faulting

Find the conjugate faults and

determine the orientations of

principal stresses.

Normal faultingNormal faulting SouthSouth NorthNorth

Normal faultingNormal faulting SouthSouth NorthNorth

σσ11

σσ11

σσ33 σσ22

Determining Sense of SlipDetermining Sense of Slip

σσ11

σσ22

σσ33

Determining Sense of SlipDetermining Sense of Slip

σσ11

Determining Sense of SlipDetermining Sense of Slip

σσ11

Determining Sense of SlipDetermining Sense of Slip

σσ11

Determining Sense of SlipDetermining Sense of Slip

σσ11

Determining Sense of SlipDetermining Sense of Slip

σσ11

σσ22

σσ33

Byerlee’sByerlee’s Law of Rock FrictionLaw of Rock Friction

µµf f = = σσss

σσnn

µµf f = coefficient of = coefficient of

sliding friction sliding friction

ByerleeByerlee verses Mohrverses Mohr--Coulomb FailureCoulomb Failure

For a given

differential stress,

brittle failure will occur

by frictional sliding on

pre-existing fractures

(if they exist) prior to

Coulomb failure

Failure ModelsFailure Models

ReferencesReferences

Slides 21, 22, 24, 39, 40Davis. G. H. and S. J. Reynolds, Structural Geology of Rocks and Regions, 2nd ed., John Wiley & Sons, New York, 776 p., 1996.

Slide 41Twiss, R. J. and E. M. Moores, Structural Geology, W. H. Freeman & Co., New York, 532 p., 1992.